Question

RAVEL Four members of the Kaplan family will take a river trip down the Colorado River in Colorado State Park. The rafting company charges $10 per day to rent the raft and $15 per person for a half-day river trip, or $100 flat rate for a half-day river trip. The raft can hold up to 10 people. A. How much will the trip cost the Kaplan family at the per person rate? B. How many people must be on the river trip to make the flat rate less expensive than the per person rate?

Answer 1

(a) $16.25

(b) 7

Explanation:

Rent of 1 raft for 1 day= $10

So, rent for 1 raft for half-day=10/2=$5

Charge for 1 person for half-day river trip =$15

Flat rate for half-day river trip=$200

(a) There is 4 member of the Kaplan on the trip.

One raft can hold up to 10 people, so, they need to take 1 raft on rent.

Rent of 1 raft for half-day =$5

Charge for 4 persons for half-day river trip =$15x4=$60

Total cost for the half-day trip for 4 persons=5+60=$65

Cost for half-day trip for 1 person= $65/4=$16.25

(B) Let there are n peoples on the river trip.

For the number of people up to 10, they need to take one boat on rent.

Total per person cost=(Cost for rent of 1 boat for half-day)+( Cost for half-day river trip)

=5+15n.

Cost for flat rate= (Cost for rent of 1 boat for half-day)+( Flat rate cost)

=5+100

The condition for which the flat-rate cost is less expensive than the per person rate cost is

`5+100<5+15n`

`\Rightarrow 100<15n`

`\Rightarrow n>(100)/(15)`

`\Rightarrow n>6(2)/(3)`

As n is the number od person which cant be a fractional value, so

n=7,8,9,... or
`n\geq7`

So, a minimum of 7 people must be on the river trip to make the flat rate less expensive than the per person rate.